128 research outputs found
Boundary conditions for augmented plane wave methods
The augmented plane wave method uses the Rayleigh-Ritz principle for basis
functions that are continuous but with discontinuous derivatives and the
kinetic energy is written as a pair of gradients rather than as a Laplacian. It
is shown here that this procedure is fully justified from the mathematical
point of view. The domain of the self-adjoint Hamiltonian, which does not
contain functions with discontinuous derivatives, is extended to its form
domain, which contains them, and this modifies the form of the kinetic energy.
Moreover, it is argued that discontinuous basis functions should be avoided.Comment: 5 pages, no figur
A many-body approach to crystal field theory
A self-consistent many-body approach is proposed to build a first-principles
crystal field theory, where crystal field parameters are calculated ab initio.
Many-body theory is used to write the energy of the interacting system as a
function of the density matrix of the noninteracting system. A variation of the
energy with respect to the density matrix gives an effective Hamiltonian that
is diagonalized to determine the density matrix providing the lowest energy.
The equations are written in terms of the Hopf algebra of functional
derivatives with respect to external fermionic sources. This approach contains
the many-body theory of Green functions as a special case, and the usual
crystal field theory as a first approximation. Therefore, it is expected to
provide good results for strongly-interacting electron systems.Comment: Equation (8) and references are correcte
Renormalization of QED with planar binary trees
The renormalized photon and electron propagators are expanded over planar
binary trees. Explicit recurrence solutions are given for the terms of these
expansions. In the case of massless Quantum Electrodynamics (QED), the relation
between renormalized and bare expansions is given in terms of a Hopf algebra
structure. For massive quenched QED, the relation between renormalized and bare
expansions is given explicitly.Comment: Uses feynmf package. 20 page
- …